Hi Andrew, welcome to iFixit Answers.
The difference between the video cable (LVDS cable) and the inverter cable :
The LVDS cable brings the video to your LCD display from the graphic card located on your logic board. The cable and the LVDS socket are located at the right side of the logic board.
The inverter cable brings the electrical power from the logic board (upper left side) to the inverter board in the display assembly and this board powers up the backlight bulb so you can see the video onscreen.
Your problem is a lightning one and the inverter cable is often the culprit in this kind of failure. From the symptoms described in your question it seems that the inverter cable is cut out somewhere in the hinge and only makes contact when the display is open at a certain angle or the cable is not well seated in the inverted board socket losing/getting contact when you're moving the display.
You'll have to carefully verify your inverter cable connections and visually check the cable for any damage where it goes inside the hinge.